Grade: 6 Unit: 5 Week: 2Content: Area Dates: 3/11 to 3/14
Theme Essential Question: How do students solve real-world and mathematical problems involving area, surface area, and volume?
Essential Questions:
Can students find the area of parallelograms?
Can students apply what they know to investigate and explore the relationship amoung the areas of triangles, rectangles, and parallelograms?
Can students find the area of triangles?
Can students apply what they know to investigate and explore the relationship between the areas of trapezoids and parallelograms?
Can students find the area of trapeziods?
Can students find the area of regular polygons?
Standards
CC.6.G.1: Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
Objectives
Students will find the area of parallelograms.
Students will investigate the relationship amoung the areas of triangles, rectangles, and parallelograms.
Students will find the area of triangles.
Students will investigate the relationship amoung the areas of trapezoids and parallelograms.
Students will find the area of trapezoids.
Students will find the area of regular polygons.
Reflections and/or Comments from your PCSSD 6th Grade Curriculum Team This is a very big week. It would be adviseable to begin the investigating part of this week during week 1 of unit 5. (Taken from Ohio Department of Education: http://education.ohio.gov/GD/DocumentManagement/DocumentDownload.aspx?DocumentID=106873 ) It is very important for students to continue to physically manipulate materials and make connections to the symbolic and more abstract aspects of geometry. Multiple strategies can be used to aid in the skill of determining the area of simple two-dimensional composite shapes. A beginning strategy should be to use rectangles and triangles, building upon shapes for which they can already determine area to create composite shapes. This process will reinforce the concept that composite shapes are created by joining together other shapes, and that the total area of the two-dimensional composite shape is the sum of the areas of all the parts.
Arizona Dept. of Education Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems. Special quadrilaterals include rectangles, squares, parallelograms, trapezoids, rhombi, and kites. Students can use tools such as the Isometric Drawing Tool on NCTM’s Illuminations site to shift, rotate, color, decompose and view figures in 2D or 3D (http://illuminations.nctm.org/ActivityDetail.aspx?ID=125)
Background Information
Recommended: For a quick overview of the standard(s) to be addressed in this lesson, see Arizona’s Content Standards Reference Materials.
Mathematical Practices 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.
Vocabulary
Math
Suggested Activities On Core Mathematics
Algebra-Area of Parallelograms Lesson 73 p145-146
Investigating-Explore Area of Triangles Lesson 74 p147-148
Algebra-Area of Trianlges Lesson 75 p149-150
Investigating-Explore Area of Trapeziods Lesson 76 p151-152
Algebra-Area of Trapeziods Lesson 77 p 153-154
Area of Regular Polygons Lesson 78 p155-156
Mastering the Common Core ABC
Ch. 11 p140-151
Teaching the Common Core Math Standards with Hands-On Activities Grades 6-8
It’s Half p54
It’s Awe-sum p55
Gizmos
JBHM
Glenco
Highly Recommended: The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.
Tasks that illustrate content standard : Diverse Learners
Theme Essential Question:
How do students solve real-world and mathematical problems involving area, surface area, and volume?
Essential Questions:
Standards
Objectives
Reflections and/or Comments from your PCSSD 6th Grade Curriculum Team
This is a very big week. It would be adviseable to begin the investigating part of this week during week 1 of unit 5.
(Taken from Ohio Department of Education: http://education.ohio.gov/GD/DocumentManagement/DocumentDownload.aspx?DocumentID=106873 )
It is very important for students to continue to physically manipulate materials and make connections to the symbolic and more abstract aspects of geometry. Multiple strategies can be used to aid in the skill of determining the area of simple two-dimensional composite shapes. A beginning strategy should be to use rectangles and triangles, building upon shapes for which they can already determine area to create composite shapes. This process will reinforce the concept that composite shapes are created by joining together other shapes, and that the total area of the two-dimensional composite shape is the sum of the areas of all the parts.
Arizona Dept. of Education
Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
Special quadrilaterals include rectangles, squares, parallelograms, trapezoids, rhombi, and kites. Students can use tools such as the Isometric Drawing Tool on NCTM’s Illuminations site to shift, rotate, color, decompose and view figures in 2D or 3D (http://illuminations.nctm.org/ActivityDetail.aspx?ID=125)
Background Information
Recommended: For a quick overview of the standard(s) to be addressed in this lesson, see Arizona’s Content Standards Reference Materials.
Assessment
1. Make sense of problems and persevere in
solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Vocabulary
Suggested Activities
On Core Mathematics
- Algebra-Area of Parallelograms Lesson 73 p145-146
- Investigating-Explore Area of Triangles Lesson 74 p147-148
- Algebra-Area of Trianlges Lesson 75 p149-150
- Investigating-Explore Area of Trapeziods Lesson 76 p151-152
- Algebra-Area of Trapeziods Lesson 77 p 153-154
- Area of Regular Polygons Lesson 78 p155-156
Mastering the Common Core ABC- Ch. 11 p140-151
Teaching the Common Core Math Standards with Hands-On Activities Grades 6-8- It’s Half p54
- It’s Awe-sum p55
Gizmos
JBHM
Glenco
Highly Recommended: The Illustrative Mathematics Project offers guidance to states, assessment consortia, testing companies, and curriculum developers by illustrating the range and types of mathematical work that students will experience in a faithful implementation of the Common Core State Standards. The website features a clickable version of the Common Core in mathematics and the first round of "illustrations" of specific standards with associated classroom tasks and solutions.Tasks that illustrate content standard :
Diverse Learners
Homework
- http://www.kutasoftware.com/free.html to print assignments on variety of topics
- See appropriate Glencoe, OnCore, JBHM, and ABC materials under suggested activities
**GIZMO
MATH FOR CHILDREN
Homework
Terminology for Teachers
Area, surface area, parallelogram, congruent, composite figure
Ethnicity/Culture | Immigration/Migration | Intercultural Competence | Socialization | Racism/Discrimination
High Yield Strategies
Similarities/Differences | Summarizing/Notetaking | Reinforcing/Recognition | Homework/Practice |
Non-Linguistic representation | Cooperative Learning | Objectives/Feedback |
Generating-Testing Hypothesis | Cues, Questions, Organizers
Resources
Professional Texts
Literary Texts
Informational Texts
Art, Music, and Media
Manipulatives
Games
Videos
Sight Words
SMART Board Lessons, Promethean Lessons
- CC.6.G.1: Area and Perimeter Review
Students explore area and perimeter by manipulating square units.- CC.6.G.1 Area of Parallelograms
The intended learning outcomes are to develop the formula for the area of a parallelogram, and to calculate the area of a parallelogram.- CC.6.G.1 Area of Figures
Used to determine the formulas for area of triangles, rectangles, and parralelograms.Other Activities, etc.
Language
Arts
Week 1
Week 2
Week 3
Week 4
6 Matrix
6 PAP Matrix
Week 1
Week 2
Week 3
Week 4
Home K-2
Home 3-6
Home 6-8
Unit 1
Unit 2
Unit 3
Unit 4